Implicit meshes

This thesis proposes novel ways both to represent the static surfaces, and to parameterize their deformations. This can be used both by automated algorithms for efficient 3–D shape reconstruction, and by graphics designers for editing and animation. Deformable 3–D models can be represented either as traditional explicit surfaces, such as triangulated meshes, or as implicit surfaces. Explicit surfaces are widely accepted because they are simple to deform and render, however fitting them involves minimizing a non-differentiable distance function. By contrast, implicit surfaces allow fitting by minimizing a differentiable algebraic distance, but they are harder to meaningfully deform and render. Here we propose a method that combines the strength of both representations to avoid their drawbacks, and in this way build robust surface representation, called implicit mesh, suitable for automated shape recovery from video sequences. This surface representation lets us automatically detect and exploit silhouette constraints in uncontrolled environments that may involve occlusions and changing or cluttered backgrounds, which limit the applicability of most silhouette based methods. We advocate the use of Dirichlet Free Form Deformation (DFFD) as generic surface deformation technique that can be used to parameterize objects of arbitrary geometry defined as explicit meshes. It is based on the small set of control points and the generalized interpolant. Control points become model parameters and their change causes model's shape modification. Using such parameterization the problem dimensionality can be dramatically reduced, which is desirable property for most optimization algorithms, thus makes DFFD good tool for automated fitting. Combining DFFD as a generic parameterization method for explicit surfaces and implicit meshes as a generic surface representation we obtained a powerfull tool for automated shape recovery from images. However, we also argue that any other avaliable surface parameterization can be used. We demonstrate the applicability of our technique to 3–D reconstruction of the human upper-body including – face, neck and shoulders, and the human ear, from noisy stereo and silhouette data. We also reconstruct the shape of a high resolution human faces parametrized in terms of a Principal Component Analysis model from interest points and automatically detected silhouettes. Tracking of deformable objects using implicit meshes from silhouettes and interest points in monocular sequences is shown in following two examples: Modeling the deformations of a piece of paper represented by an ordinary triangulated mesh; tracking a person's shoulders whose deformations are expressed in terms of Dirichlet Free Form Deformations.